Tardy Jobs Research Articles

Multi-objective multi-factory scheduling

This paper introduces a multi-factory scheduling problem with heterogeneous factories and parallel machines. This problem, as a major part of supply chain planning, includes the finding of a suitable factory for each job and the scheduling of the assigned jobs at each factory, simultaneously. For the first time, this paper studies multi-objective scheduling in the production network in which each factory has its customers and demands can be satisfied by itself or other factories. In other words, this paper assumes that jobs can transfer from the overloaded machine in the origin factory to the factory, which has fewer workloads by imposing some transportation times. For simultaneous minimization of the sum of the earliness and tardiness of jobs and total completion time, after modeling the scheduling problem as a mixed-integer linear program, the existing multi-objective techniques are analyzed and a new one is applied to our problem. Since this problem is NP-hard, a heuristic algorithm is also proposed to generate a set of Pareto optimal solutions. Also, the algorithms are proposed to improve and cover the Pareto front. Computational experiences of the heuristic algorithm and the output of the model implemented by CPLEX over a set of randomly generated test problems are reported.

Single machine scheduling problem of minimising weighted sum of maximum weighted earliness and weighted number of tardy jobs

Single machine scheduling problem of minimising weighted sum of maximum weighted earliness and weighted number of tardy jobs

Single machine scheduling problem of minimising weighted sum of maximum weighted earliness and weighted number of tardy jobs

Due to the intense competition in the markets, manufacturers are trying to deliver their customers' orders in a timely manner. Therefore, taking into account just-in-time production criteria in scheduling problems is of great importance. In this article, two criteria of maximum weighted earliness and weighted number of tardy jobs are simultaneously considered in a single machine environment for the first time. An optimal algorithm is proposed to minimise maximum weighted earliness in a single machine scheduling. Then a mixed integer programming model is presented for the bi-criteria problem. In addition, a branch-and-bound, with upper and lower bounds and dominance rules are presented to optimally solve the bi-criteria problem. To evaluate the performance of proposed methods a set of instances was generated and solved. The computational results showed that the mixed integer programming model and the branch-and-bound were capable of solving instances up to 26 and 34 jobs in size, respectively. [Submitted 1 November 2018; Accepted 1 September 2019]

Two‐Agent Single Machine Order Acceptance Scheduling Problem to Maximize Net Revenue

The paper considers two‐agent order acceptance scheduling problems with different scheduling criteria. Two agents have a set of jobs to be processed by a single machine. The processing time and due date of each job are known in advance. In the order accepting scheduling problem, jobs are allowed to be rejected. The objective of the problem is to maximize the net revenue while keeping the weighted number of tardy jobs for the second agent within a predetermined value. A mixed‐integer linear programming (MILP) formulation is provided to obtain the optimal solution. The problem is considered as an NP-hard problem. Therefore, MILP can be used to solve small problem instances optimally. To solve the problem instances with realistic size, heuristic and metaheuristic algorithms have been proposed. A heuristic method is used to determine and secure a quick solution while the metaheuristic based on particle swarm optimization (PSO) is designed to obtain the near‐optimal solution. A numerical experiment is piloted and conducted on the benchmark instances that could be obtained from the literature. The performances of the proposed algorithms are tested through numerical experiments. The proposed PSO can obtain the solution within 0.1% of the optimal solution for problem instances up to 60 jobs. The performance of the proposed PSO is found to be significantly better than the performance of the heuristic.

Nature-Inspired Metaheuristics for Two-Agent Scheduling with Due Date and Release Time

This paper delves into a two-agent scheduling problem in which two agents are competing for a single resource. Each agent has a set of jobs to be processed by a single machine. The processing time, release time, weight, and the due dates of each job are known in advance. Both agents have their objectives, which are conflicting in nature. The first agent tries to minimize the total completion time, while the second agent tries to minimize the number of tardy jobs. The two agents’ scheduling problem, an NP-hard problem, has a wide variety of applications ranging from the manufacturing industry to the cloud computing service provider. Due to the wide applicability, each variation of the problem requires a different algorithm, adapted according to the user’s requirements. This paper provides mathematical models, heuristic algorithms, and two nature-based metaheuristic algorithms to solve the problem. The algorithm’s performance was gauged against the optimal solution obtained from the AMPL-CPLEX solver for both solution quality and computational time. The outlined metaheuristics produce a solution that is comparable with a short computational time. The proposed metaheuristics even have a better solution than the CPLEX solver for medium-size problems, whereas the computation times are much less than the CPLEX solvers.

Hybrid approach for a single-batch-processing machine scheduling problem with a just-in-time objective and consideration of non-identical due dates of jobs

In this paper, we study a generalized single-batch-processing machine (SBPM) scheduling problem. Given a set of jobs that differ in terms of size, processing time and due date, the generalized SBPM problem aims to cluster the jobs into batches and process each batch one at a time on a capacitated batch-processing machine such that the total earliness and tardiness of jobs, a just-in-time objective, is minimized. We investigate the intrinsic properties of the optimal solutions of the problem, based on which an effective span-limited tree search (SLTS) heuristic is developed to find the near-optimal solutions to a restricted SBPM problem with a specified processing sequence of jobs. Varying the sequence, we embed the SLTS approach into a self-adapted genetic algorithm to further explore the solution space of the original problem. A hybrid span-limited tree search and genetic algorithm approach is proposed. The results of extensive numerical experiments on various random instances with a common due date and non-identical due dates of jobs demonstrate the effectiveness and efficiency of the proposed approaches in obtaining high-quality near-optimal solutions.

Due date optimization in multi-objective scheduling of flexible job shop production

The manuscript presents the importance of integrating mathematical methods for the determination of due date optimization parameter for maturity optimization in evolutionary computation (EC) methods in multi-objective flexible job shop scheduling problem (FJSSP). The use of mathematical modelling methods of due date optimization with slack (SLK) for low and total work content (TWK) for medium and high dimensional problems was presented with the integration into the multi-objective heuristic Kalman algorithm (MOHKA). The multi-objective optimization results of makespan, machine utilization and due date scheduling with the MOHKA algorithm were compared with two comparative multi-objective algorithms. The high capability and dominance of the EC method results in scheduling jobs for FJSSP production was demonstrated by comparing the optimization results with the results of scheduling according to conventional priority rules. The obtained results of randomly generated datasets proved the high level of job scheduling importance with respect to the interdependence of the optimization parameters. The ability to apply the presented method to the real-world environment was demonstrated by using a real-world manufacturing system dataset applied in Simio simulation and scheduling software. The optimization results prove the importance of the due date optimization parameter in highly dynamic FJSSP when it comes to achieving low numbers of tardy jobs, short job tardiness and potentially lower tardy jobs costs in relation to short makespan of orders with highly utilized production capacities. The main findings prove that multi-objective optimization of FJSSP planning and scheduling, taking into account the optimization parameter due date, is the key to achieving a financially and timely sustainable production system that is competitive in the global market.

A New Stage-Wise Control Release Policy for Semiconductor Wafer Fabrication Systems

This article presents a new closed-loop release policy: Stage-Wise Control (SWC) that maintains the overall shop floor's workload distributed into stages at a specified level by controlling the release of new jobs along the production line A simulation model is developed for the well-known Mini Fab and a real-life fab to examine the potential advantage of SWC over traditional release policies in terms of the average cycle time, the standard deviation of cycle time, WIP level, the average number of tardy jobs, and throughput. The simulation results indicate that the SWC efficiently generates high-quality schedules for the average cycle time and the standard deviation of cycle time for a prescribed throughput level. Further, several simulation experiments are carried out in this study to understand the relative performance of SWC in comparison with the existing release policies with different dispatching rules, with different system variability levels caused by machine failure, and with different segmentation method. The performance of SWC is satisfactory in most of the considered scenarios compared to the tested release policies.

Algorithms for a two-agent single machine scheduling problem to minimize weighted number of tardy jobs

This paper considers a two-agent single machine scheduling problem, with a weighted number of tardy jobs as objectives. Each agent has a finite set of jobs to be processed on a single machine. Parameters like the processing time, the due date, and the weight of jobs are known in advance. The objective is to minimize the weighted number of tardy jobs of the first agent, subject to the upper bound of the weighted number of tardy jobs of the second agent. Two metaheuristics based on Particle Swarm Optimization and Tabu Search are introduced to solve this problem. To establish the performance of the proposed meta-heuristics, a dynamic programming based exact algorithm is developed. To test the validity of the proposed algorithm, a numerical experiment is performed on randomly generated problem instances to compare the performance of the proposed algorithms.

Pareto‐optimization of three‐agent scheduling to minimize the total weighted completion time, weighted number of tardy jobs, and total weighted late work

AbstractWe consider three‐agent scheduling on a single machine in which the criteria of the three agents are to minimize the total weighted completion time, the weighted number of tardy jobs, and the total weighted late work, respectively. The problem is to find the set of all the Pareto‐optimal points, that is, the Pareto frontier, and their corresponding Pareto‐optimal schedules. Since the above problem is unary NP‐hard, we study the problem under the restriction that the jobs of the first agent have inversely agreeable processing times and weights, that is, the smaller the processing time of a job is, the greater its weight is. For this restricted problem, which is NP‐hard, we present a pseudo‐polynomial‐time algorithm to find the Pareto frontier. We also show that, for various special versions, the time complexity of solving the problem can be further reduced.

Minimizing Tardiness Penalty Costs in Job Shop Scheduling under Maximum Allowable Tardiness

In many manufacturing or service industries, there exists maximum allowable tardiness for orders, according to purchase contracts between the customers and suppliers. Customers may cancel their orders and request compensation for damages, for breach of contract, when the delivery time is expected to exceed maximum allowable tardiness, whereas they may accept the delayed delivery of orders with a reasonable discount of price within maximum allowable tardiness. Although many research works have been produced on the job shop scheduling problem relating to minimizing total tardiness, none of them have yet considered problems with maximum allowable tardiness. In this study, we solve a job shop scheduling problem under maximum allowable tardiness, with the objective of minimizing tardiness penalty costs. Two kinds of penalty costs are considered, i.e., one for tardy jobs, and the other for canceled jobs. To deal with this problem within a reasonable time at actual production facilities, we propose several dispatching rules by extending well-known dispatching rules for the job shop scheduling problem, in cooperation with a probabilistic conception of those rules. To evaluate the proposed rules, computational experiments were carried out on 300 test instances. The test results show that the suggested probabilistic dispatching rules work better than the existing rules and the optimization solver CPLEX, with a time limit.

주기적 납기일과 공통 납기일을 갖는 2-에이전트 스케줄링

We consider a single-machine scheduling problem with two agents. The objective is to minimize the objective function of agent 1 while that of agent 2 is below a given threshold. The objective function of agent 1 is the total weighted completion time, while that of agent 2 is the total weighted number of tardy jobs. Furthermore, the due date of agent 2 is assigned not to the specific job but to the position. Firstly, we show that the problem with the identical intervals between the consecutive due dates remains strongly NP-hard, even if the weights of jobs of agent 2 are identical. Finally, we proved the weak NP-hardness of the problem with a common due date.

Defining accurate delivery dates in make to order job-shops managed by workload control

Workload control (WLC) is a lean oriented system that reduces queues and waiting times, by imposing a cap to the workload released to the shop floor. Unfortunately, WLC performance does not systematically outperform that of push operating systems, with undersaturated utilizations levels and optimized dispatching rules. To address this issue, many scientific works made use of complex job-release mechanisms and sophisticated dispatching rules, but this makes WLC too complicated for industrial applications. So, in this study, we propose a complementary approach. At first, to reduce queuing time variability, we introduce a simple WLC system; next we integrate it with a predictive tool that, based on the system state, can accurately forecast the total time needed to manufacture and deliver a job. Due to the non-linearity among dependent and independent variables, forecasts are made using a multi-layer-perceptron; yet, to have a comparison, the effectiveness of both linear and non-linear multi regression model has been tested too. Anyhow, if due dates are endogenous (i.e. set by the manufacturer), they can be directly bound to this internal estimate. Conversely, if they are exogenous (i.e. set by the customer), this approach may not be enough to minimize the percentage of tardy jobs. So, we also propose a negotiation scheme, which can be used to extend exogenous due dates considered too tight, with respect to the internal estimate. This is the main contribution of the paper, as it makes the forecasting approach truly useful in many industrial applications. To test our approach, we simulated a 6-machines job-shop controlled with WLC and equipped with the proposed forecasting system. Obtained performances, namely WIP levels, percentage of tardy jobs and negotiated due dates, were compared with those of a set classical benchmark, and demonstrated the robustness and the quality of our approach, which ensures minimal delays.

Multi-objective scheduling in labor-intensive manufacturing systems

In a manufacturing facility, the decision maker considers customer satisfaction as an essential priority in which customer due dates should be met. The cell loading, scheduling and the total manpower are considered among the main decisions in a manufacturing system. Three performance measures are studied in this paper and they are the number of tardy jobs, total manpower, and average flow time. Two approaches are proposed to handle such performance measures. In the first approach, lexicographical analysis is proposed to achieve the objectives, when the performance measures are not equally important. A three-phase methodology is introduced. In the first phase, a mathematical model has been used to maximize the output rate by allocating manpower to operations for several manpower levels. In the second phase, another mathematical model is developed based on the results of the first phase to minimize total manpower such that no job is tardy (i.e., the number of tardy jobs (NT = 0)). In the third phase, a mathematical model is also proposed to minimize the average flow time based on the results obtained in the first and the second phases. The second approach allows varying weights for minimizing average flow time and total manpower subject to zero tardy jobs due to considerations for customer satisfaction. Thus, a two-phase methodology is followed, and a bi-objective fuzzy mathematical model is developed. Two-phase methodology produced similar results to three-phase methodology for certain values of weights assigned to performance measures. Three-phase methodology was efficient for lexicographical analysis. Furthermore, the number of cells in the system is affected by the nature of due dates. The number of cells and total manpower increase when the due dates are tight and decrease when the due dates are relaxed.

A Scheduling Problem to Minimize Total Weighted Tardiness in the Two-Stage Assembly Flowshop

This paper considers an assembly scheduling problem which minimizes the total weighted tardiness. The system consists of multiple manufacturing machines in the first stage and an assembly machine in the second stage. A job is composed of multiple components, each component is manufactured on a dedicated machine in the first stage, and the assembly starts on the assembly machine after the completion of all the components’ manufacturing in the first stage. This paper is to try to find effective and efficient schedules to minimize the total weighted tardiness of jobs. This paper analyzes some solution properties to improve search effectiveness and efficiency. Moreover, some lower-bound procedures are derived, and then four constructive heuristics and a branch-and-bound algorithm are suggested. The performances of the derived algorithms are evaluated through numerical experiments. For the problems with no more than 15 jobs, the branch-and-bound algorithm finds the optimal solutions within 20 minutes, and the performance of the four heuristics seems to be similar. However, for problems with more than 30 jobs, HWT shows the best performance among the four heuristics except for two machines.

Energy Efficiency Improvement through Optimal Batch Sizing in Job Shop

The increasing customization of products with greater variances and smaller lot sizes, has motivated manufacturers to adopt highly dynamic production planning. The production plans not only need to adapt to the production system state changes rapidly but also need to adopt energy reduction schemes to satisfy key sustainability performance indicators. The dilemma from industry point of view is to tackle multi-faceted problem of optimising economic and environmental performance. This research aims to overcome the multi-faceted objectives of small and medium-sized enterprises (SME’s) by providing a simulation-optimisation platform that creates the best possible production plans for optimum results. The applicability of the proposed framework is demonstrated through a real-life job-shop environment with the focus on optimisation of energy as well as job tardiness.

Scheduling a proportionate flow shop of batching machines

In this paper we study a proportionate flow shop of batching machines with release dates and a fixed number m ge 2 of machines. The scheduling problem has so far barely received any attention in the literature, but recently its importance has increased significantly, due to applications in the industrial scaling of modern bio-medicine production processes. We show that for any fixed number of machines, the makespan and the sum of completion times can be minimized in polynomial time. Furthermore, we show that the obtained algorithm can also be used to minimize the weighted total completion time, maximum lateness, total tardiness and (weighted) number of late jobs in polynomial time if all release dates are 0. Previously, polynomial time algorithms have only been known for two machines.

Two-agent scheduling of unit processing time jobs to minimize total weighted completion time and total weighted number of tardy jobs

In this paper, we revisit a two-agent scheduling problem on a single machine with jobs of unit processing times. In this problem, we have two agents: agent A and agent B. Each agent has his/her own disjoint job set. The objective of agent A is to minimize the total weighted completion time, and the objective of agent B is to minimize the total weighted number of tardy jobs. The complexity of the decision version of the problem was proposed as open in Oron et al. (European Journal of Operational Research 244:86–99, 2015). We construct a reduction from a variant of Even-Odd Partition to show that this problem is NP-complete. Finally, we also propose a pseudo-polynomial algorithm and a dual FPTAS for the problem.

Two‐agent scheduling with linear resource‐dependent processing times

AbstractThis paper considers a two‐agent scheduling problem with linear resource‐dependent processing times, in which each agent has a set of jobs that compete with that of the other agent for the use of a common processing machine, and each agent aims to minimize the weighted number of its tardy jobs. To meet the due date requirements of the jobs of the two agents, additional amounts of a common resource, which may be in discrete or continuous quantities, can be allocated to the processing of the jobs to compress their processing durations. The actual processing time of a job is a linear function of the amount of the resource allocated to it. The objective is to determine the optimal job sequence and resource allocation strategy so as to minimize the weighted number of tardy jobs of one agent, while keeping the weighted number of tardy jobs of the other agent, and the total resource consumption cost within their respective predetermined limits. It is shown that the problem is ‐hard in the ordinary sense, and there does not exist a polynomial‐time approximation algorithm with performance ratio unless ; however it admits a relaxed fully polynomial time approximation scheme. A proximal bundle algorithm based on Lagrangian relaxation is also presented to solve the problem approximately. To speed up convergence and produce sharp bounds, enhancement strategies including the design of a Tabu search algorithm and integration of a Lagrangian recovery heuristic into the algorithm are devised. Extensive numerical studies are conducted to assess the effectiveness and efficiency of the proposed algorithms.

Single-machine scheduling with maintenance activities and rejection

We study the single-machine scheduling with job rejection and the additional constraint that a maintenance activity of fixed length must be performed either by a deadline or in a fixed time interval. The scheduling costs of the accepted jobs are the makespan, maximum lateness, maximum tardiness, maximum weighted completion time, total (weighted) completion time, and total (weighted) number of tardy jobs. The objective of our research is to reveal the tradeoff between the scheduling cost of the accepted jobs and the total rejection cost of the rejected jobs. After showing that three problems are binary NP-hard, combining the known results in the literature, all the problems studied in this paper are binary NP-hard. Then we present pseudo-polynomial-time algorithms for solving all the problems studied in this paper. The distinctive feature of our research is that we always obtain time-complexity results by studying some related auxiliary Pareto scheduling problems.